Codimension One Branes

TL;DR

This paper investigates codimension one p-branes in (p+2)-dimensions using superembedding, revealing on-shell and off-shell multiplet structures, and constructing equivalent actions with gauge fixing and auxiliary fields.

Contribution

It provides a detailed superembedding analysis for p=1,2,3,5,9 branes, introducing new off-shell formulations and dualities, and constructing actions with gauge fixing.

Findings

For p=3, off-shell linear multiplet arises on the worldvolume.

For p=5, the system is on-shell with a fundamental super 2-form.

For p=9, the 11D 9-brane is overconstrained, freezing the superfield.

Abstract

We study codimension one branes, i.e. p-branes in (p+2)-dimensions, in the superembedding approach for the cases where the worldvolume superspace is embedded in a minimal target superspace with half supersymmetry breaking. This singles out the cases p=1,2,3,5,9. For p=3,5,9 the superembedding geometry naturally involves a fundamental super 2-form potential on the worldvolume whose generalised field strength obeys a constraint deducible from considering an open supermembrane ending on the p-brane. This constraint, together with the embedding constraint, puts the system on-shell for p=5 but overconstrains the 9-brane in D=11 such that the Goldstone superfield is frozen. For p=3 these two constraints give rise to an off-shell linear multiplet on the worldvolume. An alternative formulation of this case is given in which the linear multiplet is dualised to an off-shell scalar multiplet. Actions are constructed for both cases and are shown to give equivalent equations of motion. After gauge fixing a local Sp(1) symmetry associated with shifts in the Sp(1)_R Goldstone modes, we find that the auxiliary fields in the scalar multiplet parametrise a two-sphere. For completeness we also discuss briefly the cases p=1,2 where the equations of motion (for off-shell multiplets) are obtained from an action principle.